$[45$ points$]$ One key issue you have to address is to help the management decide a tradeoff between customer service and staffing cost at the POS. Cashier wages are $$14/$hour and based on previous surveys the management uses a proxy for customer waiting time in the POS queue to be $$\frac{0\mathrm{.}15}{m}i\frac{n}{?}$ customer. Use $\frac{M}{M}\frac{?}{c}[15$ points$]$ and G$/$G$/$c $[15$ points$]$ queuing models to determine the "optimal" staffing level for $($a$)$ this level of footfalls; and $($b$)$ five

times as many during special events. Select the best model to use for this application and discuss the robustness of the model you select along with justification. $[15$ points$].$